Probability and the Straight
It is almost exactly twice as easy to get a straight as it is to get a flush. A straight is a decent hand, still worth being confident over. Yet, it is no match for the hands we have already studied. To find out the chances of getting a straight, we first must find out how many possible ways there are of making up a straight:
(10 X 1024) - 40 = 10,200
You will recall in the section on the straight flush there are 10 sequences that will make a straight flush (A,K,Q,J,10 through 5,4,3,2,A). For each one of these 10 we must imagine drawing the cards we need. For example, for an ace-high straight we first need to draw an ace, there are four opportunities to pick out this ace. Then there are four kings, and four opportunities to draw it, and so on throughout the ace-hight straight. Since we need five cards, we multiply our five opportunities together to get 1024. Then we multiply this by our 10 different kinds of straight. We subtract 40 to take away our 40 straight flush possibilities, which were already accounted for earlier.
To get the odds on the straight then is a simple matter of division:
10,200/2,598,960 = 1 in 255
The numerator is the number of straights possible, while the denominator is the number of all possible hands. Getting dealt four of the five cards you need for this hand can be a boon or a curse. If you are missing one of the middle cards (i.e. 8,7,_,5,4), your chances of making the hand are only 4/47. If you have the middle cards (i.e. _'8,7,6,5,_) your chances are doubled to 8/47 because you only need to draw a card on either end. This has given rise to some lexicography regarding the "inside straight".